STAT312 Lecture Notes - Probability Mass Function, Step Function, Open Set
5 Apr 2014
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, whose elements are all possible outcomes of an experiment (e. g. is all possible sequences toss a coin three times, of three. Algebra of events is a collection b of subsets ( events ) of itself, it is such that one of its elements is closed under complementation, and closed under the taking of countable unions. s). A borel eld or s and ( ) = 1 0. A probability is a function de ned on b such that. 1, and probabili- ties of disjoint countable unions are additive. The triple ( b ) is called a probability space. All the usual rules for manipulating probabilities fol- low from these axioms. e. g. ( ) if ( ) = 0, A (real valued, nite) random variable (r. v. ) is. 86 is any open subset of r, then ( ) = # of heads in the sequence. } is an event, i. e. a member of b.
